Method for reducing homonuclear broadening in magnetic resonance spectra of solids

ABSTRACT

A method for line narrowing in nuclear magnetic resonance (NMR) studies in solids is described. The method employs quasi-continuous amplitude modulation of an rf field wherein the field is eliminated at intervals for short periods of time at or about the time when the amplitude for both the maximum and minimum approach zero, these intervals creating windows where the NMR signal can be observed.

DESCRIPTION

1. Technical Field

This invention relates to a method for generating nuclear magneticresonance spectra in solids, and pertains more particularly to employingone or more quasi-continuous sinusoidally modulated rf fields whichenhance resolution of the resultant spectrum.

2. Background Art

There has been a long period of development of high resolutiontechniques for the study of nuclear magnetic resonance spectra insolids. One of the early techniques was that of Lee and Goldbergpublished in an article entitled "Nuclear-Magnetic-Resonance LineNarrowing by a Rotating rf Field", Phys. Rev., Vol. 140, No. A4, p.1261-71 (1965). This technique employed a continuously off-resonanceZeeman field in conjunction with a continuous rf field. The combinedfields produced line narrowing; however, in order to generate a highresolution NMR line spectrum it was necessary to systematically repeatthe experiment under various operating conditions.

Waugh and his co-workers were the first to appreciate that single passtechniques could be employed that would generate a response in the solidand a spectrometer signal that, upon Fourier Tranformation, would yielda high resolution NMR spectrum. This work resulted in three patents. InU.S. Pat. No. 3,474,329 the use of a constant Zeeman field with either apulsed rf field or a series of rf pulse cycles with amplitude and phasemodulation was proposed. While the pulsed rf field effectively reducesline broadening, it was difficult to regulate the pulse cycle withsufficient accuracy to assure extensive line narrowing. While thecontinuous amplitude modulation of the rf field would appear moreattractive for regulation, the schemes disclosed in U.S. Pat. No.3,474,329 did not produce the desired line narrowing. In the subsequentU.S. Pat. Nos. 3,530,373 and 3,530,374 additional rf pulse patterns weredisclosed, as well as pulse modulation of the Zeeman field. While thepulse techniques disclosed and claimed by these latter U.S. Pat. Nos.,3,530,373 and 3,530,374, produced a superior NMR spectrum to those ofU.S. Pat. No. 3,474,329 the line narrowing required more complex pulsesequences and further increased the difficulty in generation of thepulse sequences.

Yannoni et al in an article entitled "A New Coherent Averaging Effect inMagnetic Resonance: Modulation-Induced Reduction of Dipolar Coupling",Phys. Rev. Letters, Vol. 37, pp. 1230-1232 (1976) discloses that one canobtain line narrowing in NMR experiments by the use of either acontinuous Zeeman field and pulses of frequency modulated rf, or anamplitude modulated Zeeman field with a semi-continuous rf field intowhich windows are introduced by elimination of the rf field. While thecontrol required to produce these field sequences are simpler than thoseof Waugh et al described in U.S. Pat. Nos. 3,474,329; 3,530,373; and3,530,374, the information content of the resulting spectrum is lesscomplete.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1-1 and 1-2 are schematic representations of a sinusoidalvariation of the off-resonance component of the Zeeman field and aquasi-continuous amplitude modulated rf field normal to theoff-resonance component of the Zeeman field used to practice theinvention.

FIGS. 2-1, 2-2 and 2-3 are schematic representations of a sinusoidalvariation of the off-resonance component of the Zeeman field and twoassociated quasi-continuous amplitude modulated rf fields which arenormal to the off-resonance component of the Zeeman field. These fieldsare used to practice a second mode of the invention.

FIGS. 3-1 and 3-2 are schematic representations of the waveforms ofFIGS. 1-1 and 1-2 which have been shifted by a Δ h_(z) and Δ h_(rf).These shifted fields are used to practice a third mode of the invention.

FIGS. 4-1 and 4-2 are schematic representations of the waveforms ofFIGS. 1-1 and 1-2 which have been shifted by a second scheme. Thisshifting procedure is employed to practice a fourth mode of theinvention.

FIG. 5 is a schematic representation of the frequency modulation of anrf field that will produce a virtual modulation of the Zeeman field andis employed to practice a fifth mode of the invention.

FIGS. 6-1 and 6-2 are schematic representations of two quasi-continuousamplitude modulated waveforms used to practice a sixth mode of theinvention.

FIG. 7 is an electronic block diagram illustrating a system which isconnected to a probe for implementing the invention.

FIGS. 8-1 and 8-2 represent a block diagram of an rf unit suitable forproviding the waveforms required for the present invention.

FIG. 9 is a schematic representation of the NMR signal from a tunedsystem.

DISCLOSURE OF INVENTION

A method for narrowing the lines associated with the spectrum generatedby nuclear magnetic resonance in solids is described. This methodemploys quasi-continuous sinusoidal modulation of a first rf field, andat least a second modulating field which is in one of the two directionsorthogonal to the first rf field. The first field is along an axisorthogonal with respect to a z axis, where the z axis is in thedirection of the Zeeman field.

When the second modulating field is a continuous sinusoidally modulatedcomponent of the Zeeman field, the amplitude modulation of the rf fieldis adjusted so that the envelope of the modulation is sinusoidal and hasthe same period as the modulation of the Zeeman field. Discontinuitiesin the rf field result from eliminating the field for periods of about 2to 5 microseconds at or about the zero crossing of the modulationenvelope. These intervals where the rf field is eliminated are employedas observation windows for the NMR signal. Alternatively, a virtualsinusoidal variation of the Zeeman field may be employed. The virtualfield may be induced by imposing a frequency modulation of the rf field.The frequency modulation is adjusted so that the virtual amplitudemodulation is sinusoidal, having a period equal to the period ofamplitude modulation of the rf field.

When the second modulating field is an rf field orthogonal in therotating frame, i.e., 90° out of phase relative to the first rf field,the amplitude of modulation is adjusted so that the second modulating rffield has an envelope which matches the first rf field envelope. The tworf fields are alternately applied in a periodic manner.

BEST MODES FOR CARRYING OUT THE INVENTION

FIGS. 1-1 and 1-2 illustrate a first mode where the field modulationsassociated with one technique for line narrowing are relatively easy toexecute. The experiment is conducted by employing a quasi-continuoussinusoidally modulated rf field in a direction which is orthogonal tothe direction of the Zeeman field. This waveform is illustrated in FIG.1-2. A second orthogonal field is audio-modulated and applied along thez axis in the direction of the Zeeman field. This field includes acontinuous modulation of the off-resonance Zeeman component 11, which isillustrated in FIG. 1-1. The first quasi-continuous sinusoidallymodulated rf field 10 is enveloped by two sinusoidal curves, 12 and 14,180° out of phase, each of which has a period of length 1/ω_(a), whichis the same period as is employed for the sinusoidal oscillatingoff-resonance Zeeman field 11. Discontinuities in the rf field resultfrom eliminating the field for intervals 18 of about 2 to 5 microsecondsat or about the zero crossing of the modulated envelope formed by thesinusoidal curves 12 and 14. These intervals 18 where the rf field iseliminated are employed as windows for viewing the NMR signal. Thesuccessful operation of this experiment is dependent upon the relativemagnitude of the waveforms 11, 12 and 14. When the magnitude of theperturbed component of the Zeeman field 11 can be represented by##EQU1## where: H_(1z) =magnitude of the modulated Zeeman field

β=constant

ω_(a) =constant, the magnitude of which is large with respect to thewidth of an NMR line of the solid under study.

γ=gyromagnetic ratio of the nuclei

then, the magnitude of the rf field 10 should be given by ##EQU2##where: H_(1x) =magnitude of the modulated quasi-continuous rf field

It can be seen that H_(1z) and H_(1x) are in the ratio of 1:√2, thefactor of 1/√3 being employed in both cases as a normalizing function.If the above mentioned waveforms are employed, then line narrowing willoccur when the argument β is selected so as to give the zero orderBessel function a value of zero, J₀ (2β)=-2J₀ (β)≃0.

FIGS. 2-1, 2-2 and 2-3 represent a second mode; in this embodiment ofthe present invention, three modulated fields are employed. In this casea second rf field 20 is applied orthogonal to the first rf field 10 andthe off resonant component 11 of the Zeeman field. The waveforms aredepicted in FIGS. 2-1, 2-2 and 2-3. Analytically, these waveforms may bedescribed as ##EQU3##

The first two equations defining H_(1z) and H_(1x) are identical to theequations for the first mode, with the exception that the H_(1x) ismodified by a δ function which makes this waveform operable only duringthe alternate half periods. The H_(1y) waveform is the same as H_(1x)with the exception of a complementary δ function; thus the net effect ofapplying an H_(1x) and H_(1y) is to generate two modulated rf fields foralternate half cycles. Again the length of the averaging cycle is oneaudio modulation period, 1/ω_(a). Observation windows 18 are introducedby eliminating the first rf field 10 and the second rf field 20 forintervals of time of from about 2 to 5 microseconds at periodicintervals on or about what would be the zero crossing of the twomodulating envelopes had they been continuous wave functions. Thesewindows are introduced at integral numbers of 1/ω_(a). The conditionsfor successful operation of this experiment are somewhat simpler thanthe conditions for the operation of the experiment as set forth in FIGS.1-1 and 1-2. In this case, only one Bessel function must be satisfied,J₀ (2β)≃0. Hence, there has been a relaxation of the additionalrequirement set forth in the first mode that -2 J₀ (β)≃0.

Other experiments may be defined where the off-resonance Zeeman fieldhas two components, the first is as illustrated in modes 1 and 2, andthe second is an additional bias field commonly referred to as a DC biasfield, applied to the Zeeman field, as well as to the rf field. For thisthird mode, the Zeeman field of the first mode would be modified so theform would include a term not a function of t, the analyticalrepresentation of the waveform would be: ##EQU4##

Likewise, the formulation for the rf field must be modified as follows:##EQU5## Again, the ratio between the amplitudes of H_(1z) and H_(1x)remains 1:√2. As in the case of modes 1 and 2, averaging will be overone audio modulation period. In this case the averaging conditionresults in the Bessel functions being related as follows:

J_(O) (β)=J₁ (2β)≃0. This condition is somewhat simpler and ismathematically less restrictive than the condition described in mode 1.The advantage of this experiment is that a less stringent mathematicalcriterion is employed and the technique eliminates higher order terms inthe averaging process and therefore should be more effective in linenarrowing than the method of mode 1. Pictorially, the waveforms for mode3 are illustrated in FIGS. 3-1 and 3-2. FIG. 3-1 shows the Zeeman field11 which is identical to the Zeeman field 11 of mode 1 with theexception that the average value is displaced at Δ h_(z). FIG. 3-2illustrates the waveforms for the rf field 10'. Again, the envelope issinusoidal having the same amplitude and frequency as the envelope inmode 1. However, the upper branch of the envelope and lower branch ofthe envelope no longer meet at the same point in time as in mode 1. Inaddition they are separated by a Δ h_(rf) at intervals of 1/2ω_(a),1/ω_(a) and every subsequent half cycle of the modulation.

Another effective method of constructing sinusoidal modulated NMRexperients is to vary the experiment of mode 3. This 4th mode isdepicted in FIGS. 4-1 and 4-2, and simply involves changing the sign ofthe bias of the perturbing magnetic fields.

For example, the z field would have a DC bias Δ h_(z) for the first halfcycle and for the second half cycle would have a -Δ h_(z) bias.Alternating the sign of the DC component further simplifies themathematical criterion for successful averaging and results in a lessstringent mathematical criterion. The criterion is: J₁ (2β)=0 and thecondition J₀ (β)=0 of mode 3 has vanished. The conditions of mode 4produce the sharpest NMR lines and this mode is superior to thepreceding examples. However, this improvement is accomplished at thecost of increased complexity.

It is possible to perform the experiments described in modes 1, 2, 3 and4 employing virtual variations of the Zeeman field. The virtualvariations are introduced by frequency modulating the rf field. Thefrequency modulation (FM) of the rf field is described by ##EQU6##

Particularly noteworthy is the fact that the rf frequency sinusoidallyvaries about the resonant frequencies of the sample. The frequencymodulation has the same cos ω_(a) t term with the same modulatingcoefficient β. Likewise, the conditions for successfully averaging,using frequency modulation of the rf field, are identical to thoseconditions on the Bessel functions set forth in modes 1, 2, 3 and 4. Forthe purpose of illustration, if we consider the case of the first modewhere the sinusoidally modulated Zeeman field and rf fields are used,the amplitude modulation of the two fields would be given by ##EQU7##

The FM version of this experiment would have only one real field H_(1x).The H_(1z) would be virtually created by the FM of H_(1x) rf. In thiscase no explicit modulated Zeeman field is applied.

The frequency modulation of the rf field is given by ##EQU8## where thevalue of β is such that the zero order Bessel functions have thefollowing relationship:

    J.sub.0 (2β)=-2J.sub.0 (β)≃0.

This wave function is pictorially represented in FIG. 5.

All examples to date have dealt with a quasi-continuous sinusoidalmodulation of the first rf field with the second modulated field beingthe sinusoidal component of a Zeeman field, either real or virtual. Itis also possible to practice the invention by employing a second fieldwhich is an rf field orthogonal to the first rf field. The second rffield is modulated in an analogous manner to the first rf field. The tworf fields are applied in alternate half periods. This could bemathematically expressed as follows:

    H.sub.1x =[β(ω.sub.a /γ) cos ω.sub.a t]δ(0, 1/2ω.sub.a)

    H.sub.1y =[β(ω.sub.a /γ) cos ω.sub.a t]δ(1/2ω.sub.a, 1/ω.sub.a)

In this case the value of β is selected such that:

    J.sub.0 (2β)=-1/6

This method is analogous to the Waugh multipulse experiments but doesnot suffer from the degrading effects of rf pulse rise and fall phaseglitches as described by Ellett et al in Advances in Magnetic Resonance,Vol. 5, J. S. Waugh, Academic Press, N.Y. pp/117-176, (1971). Phaseglitches arise from sharp cutoff (or on) of the rf pulse. However, theamplitude of the phase glitch increases as the amplitude of the rf fieldat the time of cutoff (or on). Since the amplitude in the modulated rfexperiments described herein is small when cutoff (or on) occurs, thephase glitch problem is correspondingly less.

The waveforms for the above example are given in FIGS. 6-1 and 6-2.

In all the aforementioned NMR experiments it must be kept in mind thatbounds on the value of ω_(a) do exist. These bounds originate from theNMR relaxation physics inherent in these experiments. The argument isessentially that the "dipolar averaging" must take place in a time lessthan T₂, the spin-spin relaxation time. For a rigid lattice solid suchas CaF₂ (the classical test sample for high resolution solid NMRexperiments) T₂ ˜20 μsec. Here ω_(a) must be >50 KHz, but as a rule"subcycle averaging" relaxes this requirement so that ω_(a) has bounds50 KHz>ω_(a) >15 KHz.

Subcycle averaging is further defined in J. S. Waugh et al, Phys, Rev.Lett., Vol. 20, No. 5, p. 180-182 (1968).

This means that typical values of the perturbing fields H_(1z), H_(rfx),and H_(rfy) will be 20 to 60 gauss. All that is essential for successfulimplementation of the experiments is to adhere to the bounds and fieldratios described earlier.

FIG. 7 is an electronic block diagram illustrating a system for carryingthe invention into practice. Minicomputer 30 is tied to a logic controldevice 32 and to the rf receiver 34. The logic control determines theactivation of an rf unit 36 having four channels and a frequency source38 that can be modulated. The source 38 and the rf unit 36 drive the rfpower amplifier 40 which in turn generates a signal for interaction withthe sample 42. The response from the sample is monitored by the rfreceiver 34. It should be noted that the above diagram is similar toother coherent averaging NMR spectrometers. One important difference,however, is that this diagram has an audio source 44 which is controlledby the logic of the system, and is synchronized with the observationwindow. The audio source has a frequency which is determined by thecontrol logic 32 and the audio waveforms from this source modulate theZeeman field at the probe through the use of a set of Zeeman field coils45 in the probe 46. These Zeeman field coils 45 are employed in additionto an rf coil 48 which is used to excite the solid. The audio source isalso the sinusoidal modulation source for the rf unit which supplies tothe sample in the probe, via the rf power amplifier 40, the modulated rffields used to implement the experiments in this invention. Inexperiments where FM is used, the frequency source 38 must be capable ofFM modulation. In the absence of conducting experiments which use FMbut, for example, modulate the Zeeman field, the experiment would notrequire the frequency source that can be modulated and it would bepossible to substitute a simple crystal oscillator.

FIGS. 8-1 and 8-2 are block diagram schematics of the rf unit useable inthe experiments of this invention herein described. This rf unit isbasically a typical four channel rf unit having on/off gates 50 on eachof the channels. The gates make it possible to independently turn eachchannel A, B, C, and D on or off. The four channels are required for theimplementation of the most complex experiment shown in FIGS. 4-1 and4-2. Generally, this four channel unit can be considered to have twosubchannels comprised of channels AB and CD respectively. For theexperiment in FIGS. 4-1 and 4-2, the rf at the sample originates inalternate audio cycles, ω_(a), from subchannel AB and CD. This mode ofoperation is required because the rf field at the sample has fixed andsinusoidal modulated components. In order to switch between + and -fixed components of field (for FIG. 4-2) the output of subchannels ABand CD are biased +1/2Δ h_(rf) and -1/2Δ h_(rf).

Note that the double balanced mixers 52 must be placed in the unit sothat sinusoidally modulated rf waveforms can be generated. Theattenuators 54A, 54B, 54C, and 54D which are respectively in each of thechannels are more important than in typical high resolutionspectrometers. This is because adjustment of the rf field amplitudes isessential to correct values.

The rf delay lines 56A, 56B, 56C, and 56D are incorporated in each ofthe channels in order to adjust the phase of the rf from these channels.In the example of FIGS. 2-2 and 2-3, rf fields orthogonal to each otherare used; these delay lines permit adjustment of this condition. Otherunits in this diagram termed BA are buffer amplifiers used to gaincomplete electronic isolation of the channels from each other so thatadjustments of phase and attenuation are independent between channels.The channels A and B are combined at 57 to form the subchannel AB;similarily for channels C and D at 58. These subchannels areindependently gated by the double balanced mixers 60 for the operationpreviously described. Finally, the gated outputs of subchannels AB andCD are power combined at 62. With this unit it is possible to conductexperiments ranging from the case where one has only one sinusoidallymodulated rf envelope to the case where one has two sinusoidal modulatedenvelopes plus a DC bias field included on each. In all other ways, thisrf unit is identical to that used in traditional NMR experiments.

In general it is true that a multipulse NMR experiment only functions aswell as the spectrometer is adjusted. The adjustment of the rf fieldsfor the previously described experiments may be accomplished in a simpleand precise manner with a flexibility not normally found in multipulseNMR. The principles governing this setup procedure are similar to thoseused in "multipulse NMR experiments" except that the forced precessionduring the 1/2 period of field modulation is adjusted instead of theadjustment of a pulse.

Consider as an example the following:

We wish to adjust the rf field H_(1x) to have the following amplitude:

    H.sub.1x =K(ω.sub.a /γ)

where K is a proportionality constant, ##EQU9## and β is the modulationcoefficient defined earlier. In the case of the simple experiment wheretwo modulated fields H_(1x), and H_(1z) are employed the value of β wewant is 1.2 (i.e., J₀ (2β)=J₀ (2.4)≈0) so K=0.979.

This relation requires that the spins precess 0.979 radians during atime equal to one-half of the modulation period τ=2π/ω_(a). Since it ismuch easier to adjust for a forced precession of π/2 radians, theadjustment can be made for precisely a π/2 radian precession, but atanother audio frequency ω_(a) '. Thus:

    0.979ω.sub.a =(π/2)ω.sub.a '                (1)

    ω.sub.a '=(2/π)(0.979ω.sub.a)

    ω.sub.a '=0.623ω.sub.a                         (2)

Equations 1 and 2 tell us two things:

(1) We must shift to a setup audio modulation frequency

    ω.sub.a '=0.623ω.sub.a

for the adjustment.

(2) Setting up at ω_(a) ' for an rf field amplitude which generates aπ/2 forced precession of the spins in 1/2 cycle of ω_(a) ' will producethe required field setting. In fact a large number of 1/2 cycles, ω_(a),of the rf field may be applied to generate a long forced precession asin multipulse NMR experiments where a train of setup pulses would beused. The formula which defines the transverse spin magnetization (i.e.,observed transverse spin NMR signal) is

    I.sub.x,y =cos υ(n)I.sub.x,y (0)

    υ(n)=(π/2)((-1).sup.n -1).

In this example n refers to the nth half cycle of audio modulation.

To execute this setup procedure one need only adjust the attenuator, 54,FIGS. 8-1 and 8-2, of the rf unit channel A, while the NMR signal fromthe receiver 34 in FIG. 7, is observed. When the correct setting isreached, the NMR signal from the receiver would look like FIG. 9.

If 100 half cycles of audio modulation are used, adjustment to anaccuracy of 0.5% should be easily obtained.

Next, a similar procedure can be used for the H_(1z) adjustment. Thiscase is different in that the Zeeman field is modulated while the rffield is off. A single prepulse of rf would be used from channel B ofFIG. 8-1, to generate transverse magnetization. This is followed by atrain of Zeeman field modulation half cycles which can be adjusted bychanging the power from audio source, 44, FIG. 7, to obtain the signalof FIG. 9.

Finally, one reverts back to the operating frequency ω_(a) to achievethe correct fields for a successful experiment.

INDUSTRIAL APPLICABILITY

The present invention will be of use in the testing industry and inparticular in non-destructive testing.

It will also be useful to supplement other techniques which probe thestructure of solids.

While the present invention has been illustrated and described in termsof preferred modes, it is to be understood that these modes are by wayof illustration and not limitation and the right is reserved to allchanges and modification coming within the scope of the invention asdefined in the appended claims.

Having thus described our invention, what we claim as new, and desire tosecure by Letters Patent is:
 1. In a method of operation of a magneticresonance spectrometer employing a Zeeman field and at least oneorthogonal radio frequency (rf) field for energization of the material,the improvement comprising:varying the Zeeman field to produce asinusoidal off-resonance component of the Zeeman field of amplitude##EQU10## and of frequency ω_(a) ; where ω_(a) is a constant which islarge with respect to the width of an NMR line of the material and β isa constant; applying a first rf field normal to said off-resonancecomponent of the Zeeman field and modulating the amplitude of said rffield to produce a sinusoidal envelope of amplitude ##EQU11## and offrequency ω_(a) ; selecting β such that J₀ (2β)=-2J₀ (β)≃0; byeliminating said first rf field for about 2 to 5 microseconds at orabout the zero crossing of said sinusoidal envelope once per audio cycleto introduce discontinuities therein; and employing said discontinuitiesfor observation windows for the NMR signals.
 2. The method of claim 1further comprising:applying a second rf field orthogonal to saidoff-resonance component of said Zeeman field and to said first modulatedrf field, having an envelope with frequency ω_(a), and amplitude##EQU12## wherein said first rf field and said second rf field areapplied alternately; and selecting β such that J₀ (2β)=0.
 3. The methodof claim 1 further comprising:imposing a DC component of theoff-resonance component of the Zeeman field; and imposing an additionalamplitude modulation component for said first rf field which is theanalog to the DC component of the Zeeman field; and adjusting β suchthat J₀ (β)=J₁ (2β)≃0.
 4. The method of claim 3, wherein said DCcomponent and additional amplitude modulation DC analog reverse in signwith each period,and β is adjusted such that J₁ (2β)=0.
 5. The method ofclaim 1, 2, 3, or 4 wherein said modulation of the Zeeman field isvirtual and is induced by imposing a frequency modulation of the form##EQU13## on said rf fields, having a period 1/ω_(a) where ω₀ is aconstant.
 6. A method of operation of a magnetic resonance spectrometercomprising:amplitude modulating an envelope of a first rf field andadjusting the amplitude of said envelope of said modulation to produce asinusoidal envelope of amplitude ##EQU14## and of frequency ω_(a) ;amplitude modulating an envelope of a second rf field which is normal tosaid first rf field direction and adjusting said modulation to produce asinusoidal envelope of amplitude ##EQU15## and of frequency ω_(a) ;selecting β such that J₁ (2β)=-1/6; applying said first rf field andsaid second rf field for alternating periods of times each of saidperiods of time being 1/ω_(a) long; eliminating said first rf field andsaid second rf field every second audio cycle for about 2 to 5microseconds at or about the zero crossing of these sinusoidal envelopesto introduce discontinuities into said rf fields; and employing saiddiscontinuities for observation windows for the NMR signals.